Minimization of total tardiness on unrelated parallel machines with sequence- and machine-dependent setup times under due date constraints

The unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times in the presence of due date constraints represents an important but relatively less-studied scheduling problem in the literature. In this study, a simple iterated greedy (IG) heuristic is presented to minimize the total tardiness of this scheduling problem. The effectiveness and efficiency of the proposed IG heuristic are compared with existing algorithms on a benchmark problem dataset used in earlier studies. Extensive computational results indicate that the proposed IG heuristic is capable of obtaining significantly better solutions than the state-of-the-art algorithms on the same benchmark problem dataset with similar computational resources.     

A hybrid particle swarm optimization for parallel machine total tardiness scheduling

The parallel machine scheduling problem has received increasing attention in recent years. This research considers the problem of scheduling jobs on parallel machines with a total tardiness objective. In the view of its non-deterministic polynomial-time hard nature, the particle swarm optimization (PSO), which is inspired by the swarming or collaborative behavior of biological populations, is employed to solve the parallel machine total tardiness problem (PMTP). Since it is very hard to directly apply standard PSO to this problem, a new solution representation is designed based on real number encoding, which can conveniently convert the job sequences of PMTP to continuous position values. Moreover, in order to enhance the performance of PSO, we introduce clonal selection algorithm (CSA) into PSO and therefore propose a new CSPSO method. The incorporation of CSA can greatly improve the swarm diversity and avoid premature convergence. We further investigate three parameters of PSO and CSPSO, finding that the parameters have marginal impact on CSPSO, which indicates that CSPSO is a very stable and robust method. The performance of CSPSO is evaluated in comparison with traditional genetic algorithm (GA) and standard PSO on 250 benchmark instances. Experimental results show that CSPSO significantly outperforms GA and PSO, with obtaining the optimal solutions of 237 instances. Additionally, PSO appears more effective than GA.     

Scheduling on unrelated parallel machines with sequence- and machine-dependent setup times and due-date constraints

We consider the unrelated parallel-machine scheduling problem with sequence- and machine-dependent setup times and due-date constraints. There are N jobs, each having a due date and requiring a single operation on one of the M machines. A setup is required if there is a switch from processing one type of job to another. Due to the characteristics of machines, the processing time depends upon the job and machine on which the job is processed, and the setup time is sequence and machine dependent. In addition, certain jobs have strict due-date constraints. An effective heuristic based on a modified apparent-tardiness-cost-with-setup procedure, the simulated annealing method, and designed improvement procedures is proposed to minimize the total tardiness of this scheduling problem. Computational characteristics of the proposed heuristic are evaluated through an extensive experiment using a newly created data set. Computational results show that the proposed heuristic is able to effectively improve the initial solutions, obtained by a modified apparent-tardiness-cost-with-setup procedure, and obtains better results than a random descent heuristic.     

Minimization of maximum tardiness on unrelated parallel machines with process restrictions and setups

We consider the problem of scheduling N jobs on M unrelated parallel machines to minimize maximum tardiness. Each job has a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions for problems in small scales.     

Minimization of maximum tardiness on unrelated parallel machines with process restrictions and setups

We consider the problem of schedulingN jobs onM unrelated parallel machines to minimize maximum tardiness. Each job has a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions for problems in small scales.     

一种求解变速机调度问题的混合蚁群优化算法

针对一类变速机总加权拖期调度问题,提出一种混合蚁群优化算法.引人单机拖期调度问题中性能良好的修正预计完成时间的一种修改版本启发式规则,计算信息素初值,有利于算法跳出局部极值,并在局部搜索阶段,采用单亲遗传算法基因移位算子,有效优化当代最优解.通过均匀试验设计和统计分析,确定算法的关键参数组合,将算法应用于随机生成的不同规模的40个算例,并将其结果与同类文献中算法的优化结果进行对比分析.结果表明,在相同迭代次数下,混合算法优于对比算法.     

A Pareto evolutionary algorithm approach to bi-objective unrelated parallel machine scheduling problems

This paper addresses the unrelated parallel machine scheduling problem with job sequence- and machine-dependent setup times. The preemption of jobs is not permitted, and the optimization criteria are to simultaneously minimize total weighted flow time and total weighted tardiness. The problem has applications in industries such as TFT-LCD, automobile, and textile manufactures. In this study, a Pareto evolutionary approach is proposed to solve the bi-objective scheduling problem. The performance of this approach using different encoding and decoding schemes is evaluated and is compared with that of two multi-objective simulated annealing algorithms via a set of instances generated by a method in the literature. The experimental results indicate that the Pareto evolutionary approach using random key representation and weighted bipartite matching optimization method outperforms the other algorithms in terms of closeness metric, based on similar computation times. Additionally, although the proposed method does not provide the best distribution in terms of diversity metric, it found most of the reference solutions.     

Ant colony optimization for unrelated parallel machine scheduling

Meeting due dates is a major issue in most manufacturing systems, and one effective measure for due dates is total weighted tardiness. In this research, we consider an ant colony optimization (ACO) algorithm incorporating a number of new ideas (heuristic initial solution, machine reselection step, and local search procedure) to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense, because the single machine case is already NP-hard in the strong sense. Computational results show that the proposed ACO algorithm outperforms other existing algorithms in terms of total weighted tardiness.     

Dispatching rules for unrelated parallel machine scheduling with release dates

A simplified procedure is proposed to predict the surface integrity of complex-shape parts generated by ball-end finishing milling. Along a complex cutting path, the tool inclination may vary within a large range. A geometrical study is performed to predict the effect of the tool inclination (lead angle) on the micro-geometry of the machined surface and on the effective cutting speed. This geometrical study brings out a range of values of the lead angle for which the machined surface is damaged by cutting pull-outs. This geometrical study also brings out a range of values of the lead angle for which the effective cutting speed is null. This case corresponds to extreme values of the cutting forces and to high compressive residual stresses. These predictions are verified for a selection of tool inclinations and other cutting parameters such as cutting speed, feed per tooth and cusp height. These machining tests are performed on a high-strength bainitic steel. The experimental campaign includes milling tests with cutting forces measurements, 2-D optical micro-geometry measurements and X-ray diffraction measurements.     

A branch-and-bound parallel algorithm for single-machine total weighted tardiness problem

This paper presents the branch-and-bound algorithm for the single-machine total weighted tardiness problem. Among exact solution approaches, the branch-and-bound algorithm from Potts and Van Wassenhove solves problems of up to 40 jobs and the algorithm from Babu et al. for 50 jobs (not for all instances). We have taken advantage of the properties of permutation broken into blocks. These properties are much stronger than elimination criteria (Potts CN, Van Wassenhove LN, 1991. IIE Trans 23:346–354; Rinnoy Kan AGH, Lageweg BJ, Lenstra JK 1975 Minimizing total cost one-machine scheduling. Oper Res 26:908–972) applied so far and they allow us to eliminate many branches of the solution tree. Parallel implementation of the algorithm enables us to reduce computational time significantly and to solve larger problems. We have tested the algorithms on randomly generated instances (of up to 80 jobs) and benchmark instances taken from the OR-Library [4]. The solutions obtained have been compared with the results yielded by the best algorithms discussed in the literature. The results show that the proposed algorithm solves the problem instances with high accuracy in a very short time.     

一类并行机调度问题的动态调度算法

针对不确定制造环境中配件数量约束条件发生变化后的并行机动态调度问题,提出了一种基于操作属性模式的并行机动态调度算法.该算法针对总拖期时间性能指标的优化,根据配件负载的裕量和相邻操作的属性模式,对原调度方案的操作次序和操作上机时间进行了调整.在不同操作和设备规模下,以及不同配件数量变化幅度下进行了数值计算.数值计算结果和实际应用结果表明,该算法是有效的,具有计算复杂度低、实时性好、对原调度算法不敏感的特点.     

Parallel processor scheduling for minimizing total weighted tardiness using ant colony optimization

In the modern business environment, meeting due dates and avoiding delay penalties are very important goals that can be accomplished by minimizing total weighted tardiness. We consider a scheduling problem in a system of parallel processors with the objective of minimizing total weighted tardiness. Our aim in the present work is to develop an efficient algorithm for solving the parallel processor problem as compared to the available heuristics in the literature and we propose the ant colony optimization approach for this problem. An extensive experimentation is conducted to evaluate the performance of the ACO approach on different problem sizes with the varied tardiness factors. Our experimentation shows that the proposed ant colony optimization algorithm is giving promising results compared to the best of the available heuristics.     

Hybrid metaheuristics for unrelated parallel machine scheduling with sequence-dependent setup times

This paper proposes several hybrid metaheuristics for the unrelated parallel-machine scheduling problem with sequence-dependent setup times given the objective of minimizing the weighted number of tardy jobs. The metaheuristics begin with effective initial solution generators to generate initial feasible solutions; then, they improve the initial solutions by an approach, which integrates the principles of the variable neighborhood descent approach and tabu search. Four reduced-size neighborhood structures and two search strategies are proposed in the metaheuristics to enhance their effectiveness and efficiency. Five factors are used to design 32 experimental conditions, and ten test problems are generated for each condition. Computational results show that the proposed hybrid metaheuristics are significantly superior to several basic tabu search heuristics under all the experimental conditions.     

Dynamic parallel machine scheduling with mean weighted tardiness objective by Q-Learning

In this paper, we discuss a dynamic unrelated parallel machine scheduling problem with sequence-dependant setup times and machine–job qualification consideration. To apply the Q-Learning algorithm, we convert the scheduling problem into reinforcement learning problems by constructing a semi-Markov decision process (SMDP), including the definition of state representation, actions and the reward function. We use five heuristics, WSPT, WMDD, WCOVERT, RATCS and LFJ-WCOVERT, as actions and prove the equivalence of the reward function and the scheduling objective: minimisation of mean weighted tardiness. We carry out computational experiments to examine the performance of the Q-Learning algorithm and the heuristics. Experiment results show that Q-Learning always outperforms all heuristics remarkably. Averaged over all test problems, the Q-Learning algorithm achieved performance improvements over WSPT, WMDD, WCOVERT, RATCS and LFJ-WCOVERT by considerable amounts of 61.38%, 60.82%, 56.23%, 57.48% and 66.22%, respectively.     

Multi-machine scheduling with deterioration effects and maintenance activities for minimizing the total earliness and tardiness costs

The due date assignment has become a challenging issue related to the interaction between various participants of the supply chain. In this paper, we consider the total earliness and tardiness penalty scheduling simultaneously with the deterioration effects and maintenance activities on an unrelated parallel machine setting. We aim to determine jointly the optimal maintenance activity positions, the optimal common due date for all the jobs, and the optimal schedule to minimize the sum of the earliness and tardiness costs. If the number of machines is fixed, we introduce a polynomial time algorithm for solving the problem. We also propose an efficient polynomial time algorithm with a lower order time complexity for finding the optimal solution of a special case of the problem.     

Efficient bi-objective ant colony approach to minimize total tardiness and system unavailability for a parallel machine scheduling problem

In recent years, decision makers give more importance to the maintenance function, viewing its substantial contribution to business productivity. However, most literature on scheduling studies does not take into account maintenance planning when implementing production schedules. The achievement of production plan without taking into account maintenance activities increases the probability of machine breakdowns, and inversely, considering maintenance actions in production planning elongates the achievement dates of orders and affects deadlines. In this paper, we propose a bi-objective model to deal with production scheduling and maintenance planning problems simultaneously. The performance criteria considered for production and maintenance are, respectively, the total tardiness and the unavailability of the production system. The start times of preventive maintenance actions and their number are not fixed in advance but considered, with the execution dates of production tasks, as decisions variables of the problem. The solution of the integrated model is based on multi-objective ant colony optimization approach. The proposed algorithm (Pareto ant colony optimization) is compared, on the basis of several metrics, with well-known multi-objective genetic algorithms, namely NSGA-II and SPEA 2, and a hybrid particle swarm optimization algorithm. Interesting results are obtained via empirical study.     

A heuristic algorithm for the just-in-time single machine scheduling problem with setups: a comparison with simulated annealing

This paper addresses the single machine early/tardy problem with unrestricted common due date and sequence-dependent setup times. Two algorithms are introduced to reach near-optimum solutions: the SAPT, a heuristic tailored for the problem, and a simulated annealing (SA) algorithm. It will be shown that SA provides solutions with slightly better quality; however, SAPT requires much less computational time. SAPT-SA is a hybrid heuristic that combines both approaches to obtain high quality solutions with low computational cost. Solutions provided by the three algorithms were compared to optimal solutions for problems with up to 25 jobs and to each other for larger problems.     

Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms

The concept of parallel machines has been widely used in manufacturing. This article proposes a genetic algorithm (GA) approach to minimize total tardiness of a set of tasks for identical parallel machines and worker assignment to machines. A spreadsheet-based GA approach is presented to solve the problem. A domain-independent general purpose GA is used, which is an add-in to the spreadsheet software. The paper demonstrates an adaptation of the proprietary GA software to the problem of minimizing total tardiness for the worker assignment scheduling problem for identical parallel machine models. Two 100 I/P/n/m/W problems taken from Hu (Int J Adv Manuf Technol 23:383–388, 2004, Int J Adv Manuf Technol 29:165–169, 2006) for a similar study are simulated. The performance of GA is superior to SES-A/LMC approach used by Hu and very close to the Exhaustive search procedure. It is shown that the spreadsheet GA implementation makes it very easy to adapt the problem for any set of objective measures without changing the actual model. Empirical analysis has been carried out to study the effect of GA parameters, namely, crossover rate, mutation rate, and the population size.